Correlation Network Analysis¶

Gene network analysis is a method designed to identify sub-networks (modules) of correlated genes, which are likely to be co-expressed. This can be helpful in identification of sub-networks (modules) of genes that contribute to disease. In this example, we will cover how to create a pairwise correlation matrix of genes, as well as how to associate them with disease.

In [1]:

import pandas as pd
import numpy as np
import scanpy as sc
import anndata
import networkx as nx
import scipy.cluster.hierarchy as sch
import matplotlib.pyplot as plt
import json
import scipy
from sklearn.decomposition import PCA
from scipy.stats import pearsonr
from scipy.spatial.distance import pdist, squareform
from statsmodels.stats.multitest import multipletests
import random

import pandas as pd import numpy as np import scanpy as sc import anndata import networkx as nx import scipy.cluster.hierarchy as sch import matplotlib.pyplot as plt import json import scipy from sklearn.decomposition import PCA from scipy.stats import pearsonr from scipy.spatial.distance import pdist, squareform from statsmodels.stats.multitest import multipletests import random

In [2]:

#Load in the required data
datExpr = pd.read_csv('/ReCoDE-Gene-Network-Analysis/data/data/Bcell_datExpr_pseudobulk.csv', index_col = 0)
metadata = pd.read_csv('/ReCoDE-Gene-Network-Analysis/data/data/Bcell_metadata_pseudobulk.csv', index_col = 0)

#Load in the required data datExpr = pd.read_csv('/ReCoDE-Gene-Network-Analysis/data/data/Bcell_datExpr_pseudobulk.csv', index_col = 0) metadata = pd.read_csv('/ReCoDE-Gene-Network-Analysis/data/data/Bcell_metadata_pseudobulk.csv', index_col = 0)

In [3]:

datExpr

datExpr

Out[3]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
donor_id
CH-20-001	6.380902	0.00000	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	53.239480	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	21.632603	17.641195
CH-20-002	12.606751	2.33599	0.000000	0.000000	0.00000	0.000000	1.089918	0.000000	1.158743	1.173824	...	0.000000	112.643970	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	45.432410	22.809190
CH-20-004	12.302510	0.00000	0.000000	21.512184	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	42.873410	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	15.570595	20.173725
CH-20-005	18.603716	1.16925	1.232658	4.975880	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	1.112746	190.337740	0.000000	0.0000	1.191559	0.000000	0.000000	0.000000	6.931139	1.071742
CH-21-002	13.705297	0.00000	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	44.942260	0.000000	0.0000	0.000000	0.000000	0.000000	1.323198	0.000000	0.000000
CH-21-006	4.377715	0.00000	0.000000	23.782143	0.00000	0.000000	0.000000	0.000000	1.023552	0.000000	...	0.000000	12.741602	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	5.349793	12.981407
CH-21-008	18.058025	0.00000	0.000000	44.614340	0.00000	1.201673	0.000000	0.000000	0.000000	0.000000	...	0.000000	76.893720	0.000000	0.0000	0.000000	0.000000	0.000000	1.080360	1.188176	2.377049
CH-21-013	21.395964	0.00000	0.000000	30.426510	0.00000	0.000000	1.235703	0.000000	0.000000	0.000000	...	0.000000	54.458330	0.000000	0.0000	0.000000	0.000000	1.117969	1.236817	23.543072	53.250420
CH-21-014	13.436963	0.00000	0.000000	11.067089	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	32.248600	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	17.709280	21.636190
CH-21-017	22.916807	0.00000	0.000000	9.076924	0.00000	0.000000	0.000000	0.000000	2.478934	0.000000	...	0.000000	188.600070	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	49.114600	40.454937
CH-21-020	197.794700	0.00000	0.000000	122.788270	0.00000	0.000000	0.000000	0.000000	1.047435	0.000000	...	0.000000	197.616580	0.000000	0.0000	0.000000	0.000000	0.000000	0.765914	88.202680	173.938080
CH-21-021	13.898113	0.00000	0.000000	11.169237	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	20.431047	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	11.017612	21.158054
CH-21-028	7.210576	0.00000	1.066841	1.321003	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	57.428060	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	2.989963	0.000000
CH-21-029	9.007506	0.00000	0.000000	1.928462	1.21185	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	157.941900	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	3.745571	2.051687
CH-21-031	30.211197	0.00000	0.000000	40.325450	0.00000	0.000000	0.000000	2.130981	0.000000	0.000000	...	1.244156	12.550498	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	1.227465	0.906813
CH-21-033	21.972580	0.00000	0.000000	84.504500	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	152.658000	1.167664	1.2505	0.000000	1.199426	0.000000	0.000000	45.661453	142.600740
CH-21-034	54.934030	0.00000	0.000000	147.552780	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.886594	167.975900	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	0.000000	1.075679
CH-21-036	17.018766	0.00000	0.000000	2.483573	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	88.924920	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	39.051266	10.004631
CH-21-037	150.473450	0.00000	0.000000	53.255013	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	38.325650	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	33.786545	58.778214
CH-21-046	9.337872	0.00000	0.000000	28.949800	0.00000	1.123670	0.000000	0.000000	0.000000	0.000000	...	0.000000	28.600826	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	9.238980	12.119887
CH-21-073	4.982193	0.00000	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	40.201653	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	27.179262	2.954510
CH-21-074	3.954194	0.00000	0.000000	0.000000	0.00000	0.000000	0.000000	1.127058	0.000000	0.000000	...	0.000000	18.354240	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	6.401694	2.069999
CH-21-077	33.969110	0.00000	0.000000	3.333775	0.00000	0.000000	0.000000	0.000000	1.115637	0.000000	...	0.000000	161.007570	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	1.646068	0.000000
CH-21-079	7.030363	0.00000	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	40.449474	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	18.332941	11.980942

24 rows × 1000 columns

In [4]:

metadata

metadata

Out[4]:

	nCount_RNA	nFeature_RNA	donor_id.1	MUTATION	percent.mt	scType_celltype	tissue_type	cell_type	tissue	development_stage	male	female	CH	normal	DNMT3A	TET2	NoMutation
donor_id
CH-20-001	2490.0	1403	CH-20-001	DNMT3A R882C	6.119578	Naive B cells	tissue	B cell	blood	60	1	0	1	0	1	0	0
CH-20-002	1192.0	629	CH-20-002	DNMT3A R729W (4%), DNMT3A R736C (2%)	3.803975	Naive B cells	tissue	B cell	blood	68	1	0	1	0	1	0	0
CH-20-004	1833.0	985	CH-20-004	TET2 R1516X (30%), TET2 Q659X (29%), SRSF2 P95...	5.335196	Naive B cells	tissue	B cell	blood	85	1	0	1	0	0	1	0
CH-20-005	1966.0	886	CH-20-005	TET2 V1900F (2%)	5.314136	Naive B cells	tissue	B cell	blood	58	0	1	1	0	0	1	0
CH-21-002	1912.0	938	CH-21-002	none	5.657238	Naive B cells	tissue	B cell	blood	48	0	1	0	1	0	0	1
CH-21-006	1356.0	709	CH-21-006	DNMT3A R882H (13%)	5.211849	Naive B cells	tissue	B cell	blood	67	0	1	1	0	1	0	0
CH-21-008	1117.0	575	CH-21-008	none	8.398348	Naive B cells	tissue	B cell	blood	70	0	1	0	1	0	0	1
CH-21-013	1321.0	816	CH-21-013	none	4.663212	Naive B cells	tissue	B cell	blood	73	1	0	0	1	0	0	1
CH-21-014	1064.0	623	CH-21-014	SRSF2 P95R (40%), TET2 L957Ifs*15 (51%)	4.146577	Naive B cells	tissue	B cell	blood	74	1	0	1	0	0	1	0
CH-21-017	1880.0	953	CH-21-017	DNMT3A R882H (20%), IDH2 R140Q (10%), TP53 R27...	6.519922	Naive B cells	tissue	B cell	blood	65	1	0	1	0	1	0	0
CH-21-020	5325.0	2286	CH-21-020	none	5.631046	Naive B cells	tissue	B cell	blood	61	1	0	0	1	0	0	1
CH-21-021	1671.0	943	CH-21-021	none	3.214286	Naive B cells	tissue	B cell	blood	83	1	0	0	1	0	0	1
CH-21-028	1690.0	866	CH-21-028	none	6.053894	Naive B cells	tissue	B cell	blood	89	0	1	0	1	0	0	1
CH-21-029	2180.0	1073	CH-21-029	TET2 G68X (2%)	2.570194	Naive B cells	tissue	B cell	blood	83	0	1	1	0	0	1	0
CH-21-031	1592.0	887	CH-21-031	none	6.734398	Naive B cells	tissue	B cell	blood	78	0	1	0	1	0	0	1
CH-21-033	2219.0	1138	CH-21-033	TET2 (33%)	5.670567	Naive B cells	tissue	B cell	blood	81	1	0	1	0	0	1	0
CH-21-034	2010.0	974	CH-21-034	DNMT3A Q816X (8%)	7.937365	Naive B cells	tissue	B cell	blood	39	0	1	1	0	1	0	0
CH-21-036	2686.0	1337	CH-21-036	DNMT3A splice (7%)	3.909544	Naive B cells	tissue	B cell	blood	91	1	0	1	0	1	0	0
CH-21-037	3546.0	1645	CH-21-037	TET2 (6.2%)	4.473764	Naive B cells	tissue	B cell	blood	71	1	0	1	0	0	1	0
CH-21-046	1918.0	907	CH-21-046	DNMT3A W305X (24%)	4.807084	Naive B cells	tissue	B cell	blood	80	1	0	1	0	1	0	0
CH-21-073	2148.0	1096	CH-21-073	SRSF2 (33%), TET2 Y1245Lfs*22 (27%), TET2 Q742...	5.174489	Naive B cells	tissue	B cell	blood	77	1	0	1	0	0	1	0
CH-21-074	1322.0	708	CH-21-074	TET2 C1378Y (23%)	3.328561	Naive B cells	tissue	B cell	blood	70	1	0	1	0	0	1	0
CH-21-077	1715.0	934	CH-21-077	DNMT3A R749C (9.1%)	6.539510	Naive B cells	tissue	B cell	blood	50	0	1	1	0	1	0	0
CH-21-079	1354.0	793	CH-21-079	DNMT3A M880V (5%)	6.386293	Naive B cells	tissue	B cell	blood	78	1	0	1	0	1	0	0

Correlation is a statistical measure that describes the extent to which two variables change together. It indicates the strength and direction of a linear relationship between two variables. Correlation analysis for coexpression networks is a method used to study the relationships between genes or proteins by analysing their expression levels across various conditions, tissues, or time points. We will be exploring correlation based co-expression networks within this exercise.

Step 1: Calculate Correlation¶

In [5]:

#You can use the corr function to calculate pairwise pearson correlations between the genes.
correlation_matrix = datExpr.corr()

#You can use the corr function to calculate pairwise pearson correlations between the genes. correlation_matrix = datExpr.corr()

Lets view the correlation matrix. You will see that there is a diagonal of the value 1, due to the calculating the correlation between the same gene.

In [6]:

correlation_matrix

correlation_matrix

Out[6]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
ISG15	1.000000	-0.092502	-0.106168	0.645245	-0.093365	-0.102921	-0.080086	-0.052127	0.180437	-0.076886	...	0.029464	0.334351	-0.034003	-0.034003	-0.049428	-0.034003	-0.036643	0.187654	0.602785	0.673038
LINC01342	-0.092502	1.000000	0.281837	-0.183851	-0.059383	-0.085815	0.556591	-0.081739	0.227693	0.890407	...	0.186025	0.251452	-0.059383	-0.059383	0.416022	-0.059383	-0.059383	-0.124612	0.173334	-0.071186
TTLL10-AS1	-0.106168	0.281837	1.000000	-0.181582	-0.062692	-0.090597	-0.090459	-0.086293	-0.140100	-0.062692	...	0.383858	0.218250	-0.062692	-0.062692	0.743859	-0.062692	-0.062692	-0.131555	-0.209975	-0.179643
TNFRSF18	0.645245	-0.183851	-0.181582	1.000000	-0.133171	0.079331	-0.082125	-0.003088	-0.006450	-0.143499	...	0.295032	0.385228	0.309068	0.309068	-0.116850	0.309068	0.019452	0.157654	0.316701	0.583206
CALML6	-0.093365	-0.059383	-0.062692	-0.133171	1.000000	-0.062831	-0.062735	-0.059846	-0.097162	-0.043478	...	-0.077984	0.248300	-0.043478	-0.043478	-0.043478	-0.043478	-0.043478	-0.091237	-0.159078	-0.117442
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TMEM255A	-0.034003	-0.059383	-0.062692	0.309068	-0.043478	-0.062831	-0.062735	-0.059846	-0.097162	-0.043478	...	-0.077984	0.230799	1.000000	1.000000	-0.043478	1.000000	-0.043478	-0.091237	0.256518	0.562305
SMIM10L2B-AS1	-0.036643	-0.059383	-0.062692	0.019452	-0.043478	-0.062831	0.737278	-0.059846	-0.097162	-0.043478	...	-0.077984	-0.094460	-0.043478	-0.043478	-0.043478	-0.043478	1.000000	0.523393	0.037215	0.130174
IL9R_ENSG00000124334	0.187654	-0.124612	-0.131555	0.157654	-0.091237	0.269090	0.339578	-0.125584	-0.073338	-0.091237	...	-0.163645	-0.006889	-0.091237	-0.091237	-0.091237	-0.091237	0.523393	1.000000	0.050801	0.197187
DDX3Y	0.602785	0.173334	-0.209975	0.316701	-0.159078	-0.210786	0.200461	-0.228903	0.451454	0.254247	...	-0.301277	0.402058	0.256518	0.256518	-0.127493	0.256518	0.037215	0.050801	1.000000	0.819119
EIF1AY	0.673038	-0.071186	-0.179643	0.583206	-0.117442	-0.134538	0.088271	-0.166598	0.225645	-0.017051	...	-0.219688	0.382712	0.562305	0.562305	-0.122181	0.562305	0.130174	0.197187	0.819119	1.000000

1000 rows × 1000 columns

Step 2: Calculate Distance Matrix¶

Now that we have the correlation matrix, we need to calculate the distance matrix. A distance matrix is a mathematical representation that captures the pairwise distances between a set of objects. In hierarchical clustering, distance matrices are used to determine which objects to merge or split based on their pairwise distances. So, we will be using the distance matrix in order to calculate clusters between genes, which will form our networks. These are commonly also called communities.

In [7]:

# Perform hierarchical clustering using the dissimilarity values
distance_matrix = 1 - correlation_matrix  # Convert correlation to distance

#The linkage function is used to perform hierarchical clustering on the distance matrix. 
linkage_matrix = sch.linkage(distance_matrix, method='average')

# Plot the dendrogram
plt.figure(figsize=(10, 6))
dendrogram = sch.dendrogram(linkage_matrix)
plt.title('Hierarchical Clustering Dendrogram')
plt.xlabel('Sample Index')
plt.ylabel('Distance')
plt.show()

# Perform hierarchical clustering using the dissimilarity values distance_matrix = 1 - correlation_matrix # Convert correlation to distance #The linkage function is used to perform hierarchical clustering on the distance matrix. linkage_matrix = sch.linkage(distance_matrix, method='average') # Plot the dendrogram plt.figure(figsize=(10, 6)) dendrogram = sch.dendrogram(linkage_matrix) plt.title('Hierarchical Clustering Dendrogram') plt.xlabel('Sample Index') plt.ylabel('Distance') plt.show()

Step 3: Threshold Correlations¶

Due to all of the vast correlations, the networks will be very messy each having lots of edges with varying correlation strengths. Not all of these are of interest, such as weak correlations. So we would solely like to focus on the strong correlations.

In [8]:

# Define threshold for significant edges (you can adjust this based on your requirement)
threshold = 1

# Threshold the correlation matrix to determine significant edges
significant_edges = correlation_matrix > threshold

# Define threshold for significant edges (you can adjust this based on your requirement) threshold = 1 # Threshold the correlation matrix to determine significant edges significant_edges = correlation_matrix > threshold

Lets have a look at the significant_edges dataframe. You can now see that this produces a boolean dataframe which states whether the values are greater than the threshold or not.

In [9]:

significant_edges

significant_edges

Out[9]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
ISG15	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
LINC01342	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
TTLL10-AS1	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
TNFRSF18	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
CALML6	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TMEM255A	False	False	False	False	False	False	False	False	False	False	...	False	False	True	False	False	False	False	False	False	False
SMIM10L2B-AS1	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
IL9R_ENSG00000124334	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
DDX3Y	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
EIF1AY	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False

1000 rows × 1000 columns

Step 4: Construct Network¶

networkx is a python library designed for network analysis. Construct the network from significant edges.

In [10]:

G = nx.Graph()

# Loop through significant edges and add edges to the graph
for i in range(significant_edges.shape[0]):
    for j in range(significant_edges.shape[1]):
        if significant_edges.values[i, j]:
            gene1 = significant_edges.index[i]
            gene2 = significant_edges.columns[j]
            
            # Find the position of gene1 and gene2 in the correlation matrix
            i_corr = np.where(correlation_matrix.index == gene1)[0][0]
            j_corr = np.where(correlation_matrix.columns == gene2)[0][0]
            
            # Add the edge to the graph
            G.add_edge(gene1, gene2, weight=correlation_matrix.iloc[i_corr, j_corr])

# Display the number of nodes and edges in the graph
print("Number of nodes:", G.number_of_nodes())
print("Number of edges:", G.number_of_edges())

G = nx.Graph() # Loop through significant edges and add edges to the graph for i in range(significant_edges.shape[0]): for j in range(significant_edges.shape[1]): if significant_edges.values[i, j]: gene1 = significant_edges.index[i] gene2 = significant_edges.columns[j] # Find the position of gene1 and gene2 in the correlation matrix i_corr = np.where(correlation_matrix.index == gene1)[0][0] j_corr = np.where(correlation_matrix.columns == gene2)[0][0] # Add the edge to the graph G.add_edge(gene1, gene2, weight=correlation_matrix.iloc[i_corr, j_corr]) # Display the number of nodes and edges in the graph print("Number of nodes:", G.number_of_nodes()) print("Number of edges:", G.number_of_edges())

Number of nodes: 270
Number of edges: 1291

Step 5: Network Analysis¶

Analyse the network: For example, you can identify clusters/modules using community detection algorithms

In [11]:

communities = nx.algorithms.community.greedy_modularity_communities(G)

communities = nx.algorithms.community.greedy_modularity_communities(G)

In [12]:

communities

communities

Out[12]:

[frozenset({'AKAP14',
            'ANKRD29',
            'ANO1',
            'ARHGAP23',
            'ARHGEF39',
            'C21orf62',
            'CC2D2B',
            'CCNA1',
            'CDH6',
            'CFAP99',
            'CNKSR3',
            'CYYR1',
            'DBX2',
            'DENND6A-AS1',
            'DEPDC7',
            'DTNA',
            'FNDC5',
            'GJB6',
            'GJC2',
            'GNG12',
            'HCG9',
            'HYDIN',
            'IGLC4',
            'IGLV5-37',
            'KLHL13',
            'KRT2',
            'LAMA2',
            'LCN2',
            'LIM2',
            'LIN28A',
            'LINC00640',
            'LINC00997',
            'LINC01133',
            'LINC01832',
            'LINC01891',
            'LINC02267',
            'LNCOC1',
            'MGAM',
            'MOBP',
            'MUCL3',
            'NGFR',
            'NKD2',
            'NKX6-3',
            'OPA1-AS1',
            'OR2B11',
            'PHACTR3',
            'PLSCR2',
            'PRLR',
            'PRRT3-AS1',
            'PTGES',
            'RARRES2',
            'REG1A',
            'RNF182',
            'SLC10A5',
            'SLC17A7',
            'SLC26A8',
            'SLC28A2',
            'SLC2A4',
            'SLC6A3',
            'SRRM5',
            'STAP2',
            'STARD6',
            'TDRD1',
            'TDRP',
            'TECTA',
            'TMEM255A',
            'TMEM72-AS1',
            'ZC2HC1B',
            'ZNF462',
            'ZSCAN10'}),
 frozenset({'ACTN3',
            'ACVR2B-AS1',
            'C10orf105',
            'CALML6',
            'CDC42EP1',
            'DLGAP2',
            'DPYD-IT1',
            'EPHB2',
            'ESCO2',
            'FAM174A-DT',
            'FOXD3',
            'H3C8',
            'ICA1-AS1',
            'LINC01986',
            'LINC02348',
            'LINC02569',
            'LINC02615',
            'MROH8',
            'PAPPA-AS1',
            'PDK4-AS1',
            'PRKD3-DT',
            'RAB6C',
            'RGPD6',
            'SLC12A3',
            'TFAP2A',
            'UBE2Q2P16',
            'WNT3A',
            'ZNF503'}),
 frozenset({'BSN',
            'C12orf71',
            'CADM4',
            'CCK',
            'CLGN',
            'COPDA1',
            'DAGLA',
            'DBH-AS1',
            'FAM20C',
            'IGHV3-32',
            'IGKV3D-11',
            'KCNQ4',
            'LGALSL-DT',
            'LINC01050',
            'LINC01503',
            'NKX6-2',
            'PGAM2',
            'PPP1R9A-AS1',
            'PRR15',
            'REEP1',
            'RGL3',
            'SMIM17',
            'SPDYE21',
            'STON2',
            'TWIST2',
            'ZNF32-AS2',
            'ZSCAN2-AS1'}),
 frozenset({'ALDH8A1',
            'CUX2',
            'EPHA2',
            'GLP2R',
            'IGHV3-69-1',
            'IGHV3-73',
            'MAG',
            'MEX3B',
            'MOCS1',
            'MTOR-AS1',
            'MYO3B',
            'OR2AK2',
            'PCSK1',
            'PITPNM2-AS1',
            'PTPRD-AS1',
            'SCT',
            'SLC5A5',
            'ST8SIA5',
            'TAF1L',
            'TKTL2',
            'ZNF474'}),
 frozenset({'ADGRG3',
            'BRME1',
            'CFAP141',
            'CLEC1B',
            'COL11A2',
            'DPYSL4',
            'FAM186B',
            'FSTL1',
            'LDHAL6A',
            'LINC00200',
            'LINC01108',
            'LINC02880',
            'PRUNE2',
            'RARRES1',
            'SCARF2',
            'SMIM10L2B-AS1',
            'TRBJ2-4',
            'UBL4B',
            'VWA5B1',
            'ZNF491'}),
 frozenset({'ACTL7B',
            'AMPD1',
            'ATP8A1-DT',
            'DEPTOR-AS1',
            'EDNRB-AS1',
            'H3C12',
            'HEATR4',
            'IGKV1D-13',
            'IGKV2D-30',
            'LINC01823',
            'LINC01990',
            'MIPOL1',
            'MIR130AHG',
            'OR6C6',
            'SLC16A14',
            'SLC1A2-AS1',
            'SLC49A3',
            'SLC4A9',
            'TGFB2-AS1'}),
 frozenset({'C1orf50-AS1',
            'FOXI1',
            'GYS2',
            'HCG22',
            'HDHD5-AS1',
            'IGHV1-14',
            'LINC01579',
            'LINC02055',
            'LINC03021_ENSG00000254319',
            'MYLK3',
            'NAALADL2',
            'NLRP6',
            'PCDHGA3',
            'PRSS45P',
            'RNF217-AS1',
            'UNC79',
            'VSTM1',
            'VWA7'}),
 frozenset({'CASC9',
            'CCDC28A-AS1',
            'CFAP57',
            'CYP2S1',
            'FREY1',
            'GCNT3',
            'IGHV7-4-1',
            'IGLV5-45',
            'LINC00654',
            'NHS',
            'RHOXF1-AS1',
            'RNF112',
            'SLITRK5',
            'THTPA',
            'TMPRSS3',
            'TRMT9B',
            'TRPM1'}),
 frozenset({'ASIC3',
            'BHLHE22',
            'C10orf71',
            'CT69',
            'DNMBP-AS1',
            'EDAR',
            'LIF',
            'MS4A4E',
            'S100A16',
            'SLC22A1',
            'TRAV29DV5',
            'TTLL7'}),
 frozenset({'ACTA2-AS1',
            'CDH23',
            'CHRNG',
            'FAM182A',
            'LINC02660',
            'NKX6-1',
            'PACRG',
            'TAS2R39'}),
 frozenset({'ASGR2', 'GOLGA8H', 'IGKV2-26', 'LINC02057', 'LRRC49', 'TEKTIP1'}),
 frozenset({'CBY3', 'CYP2C8', 'LINC01301', 'PELP1-DT', 'PTGR1'}),
 frozenset({'DLG1-AS1', 'IQSEC2', 'KCNH6', 'LINC01980', 'LPAR4'}),
 frozenset({'DUOX2', 'HSD17B2-AS1', 'LINC01115_ENSG00000237667', 'MYO3A'}),
 frozenset({'FCN3', 'PCDHB4', 'S100A5'}),
 frozenset({'CNTNAP3', 'IGFBP2', 'USP43'}),
 frozenset({'NPM2', 'RHBDF1'}),
 frozenset({'SERTAD3-AS1', 'STXBP6'})]

In [13]:

# Initialise a new graph for community visualisation
community_graph = nx.Graph()

# Initialise a new graph for community visualisation community_graph = nx.Graph()

In [14]:

# Add edges between communities based on their connectivity
for i, community in enumerate(communities):
    for node in community:
        community_graph.add_node(node)
        for neighbor in G.neighbors(node):
            if neighbor in community:
                community_graph.add_edge(node, neighbor, weight=G[node][neighbor]['weight'])

# Add edges between communities based on their connectivity for i, community in enumerate(communities): for node in community: community_graph.add_node(node) for neighbor in G.neighbors(node): if neighbor in community: community_graph.add_edge(node, neighbor, weight=G[node][neighbor]['weight'])

In [15]:

# Initialise an empty list to store separated communities
separated_communities = []

# Iterate over the detected communities
for community in communities:
    # Convert the set of nodes into a list and append it to the list of lists
    separated_communities.append(list(community))

# Initialise an empty list to store separated communities separated_communities = [] # Iterate over the detected communities for community in communities: # Convert the set of nodes into a list and append it to the list of lists separated_communities.append(list(community))

In [16]:

# Print or use the separated communities as needed
print(separated_communities)

# Print or use the separated communities as needed print(separated_communities)

[['NKX6-3', 'ZC2HC1B', 'ZSCAN10', 'HCG9', 'CC2D2B', 'DBX2', 'MOBP', 'STAP2', 'LCN2', 'ZNF462', 'TMEM72-AS1', 'LNCOC1', 'SLC28A2', 'SLC10A5', 'SRRM5', 'SLC17A7', 'OPA1-AS1', 'DEPDC7', 'LIN28A', 'SLC6A3', 'GJB6', 'TMEM255A', 'IGLC4', 'LINC00640', 'DENND6A-AS1', 'FNDC5', 'LAMA2', 'CYYR1', 'CNKSR3', 'RNF182', 'TECTA', 'KRT2', 'PRRT3-AS1', 'LINC02267', 'MUCL3', 'CFAP99', 'CCNA1', 'SLC26A8', 'GNG12', 'PHACTR3', 'LINC01133', 'C21orf62', 'ANKRD29', 'NGFR', 'NKD2', 'GJC2', 'LIM2', 'ANO1', 'LINC00997', 'STARD6', 'ARHGAP23', 'HYDIN', 'KLHL13', 'IGLV5-37', 'PLSCR2', 'TDRP', 'REG1A', 'LINC01832', 'ARHGEF39', 'CDH6', 'LINC01891', 'MGAM', 'AKAP14', 'TDRD1', 'PRLR', 'RARRES2', 'SLC2A4', 'OR2B11', 'DTNA', 'PTGES'], ['ACTN3', 'PDK4-AS1', 'C10orf105', 'ACVR2B-AS1', 'LINC02348', 'DPYD-IT1', 'UBE2Q2P16', 'PRKD3-DT', 'LINC01986', 'CALML6', 'EPHB2', 'PAPPA-AS1', 'DLGAP2', 'MROH8', 'RAB6C', 'ZNF503', 'H3C8', 'LINC02569', 'CDC42EP1', 'TFAP2A', 'ESCO2', 'WNT3A', 'SLC12A3', 'RGPD6', 'ICA1-AS1', 'FOXD3', 'LINC02615', 'FAM174A-DT'], ['IGHV3-32', 'LINC01050', 'STON2', 'CLGN', 'CCK', 'RGL3', 'COPDA1', 'PPP1R9A-AS1', 'SPDYE21', 'BSN', 'PRR15', 'IGKV3D-11', 'C12orf71', 'SMIM17', 'FAM20C', 'KCNQ4', 'PGAM2', 'DAGLA', 'NKX6-2', 'REEP1', 'LGALSL-DT', 'ZNF32-AS2', 'ZSCAN2-AS1', 'TWIST2', 'LINC01503', 'CADM4', 'DBH-AS1'], ['MAG', 'MOCS1', 'ALDH8A1', 'MTOR-AS1', 'MEX3B', 'MYO3B', 'GLP2R', 'SCT', 'TAF1L', 'IGHV3-73', 'OR2AK2', 'PTPRD-AS1', 'ST8SIA5', 'PITPNM2-AS1', 'EPHA2', 'TKTL2', 'SLC5A5', 'PCSK1', 'CUX2', 'IGHV3-69-1', 'ZNF474'], ['LINC02880', 'COL11A2', 'SCARF2', 'ADGRG3', 'ZNF491', 'CFAP141', 'FSTL1', 'TRBJ2-4', 'SMIM10L2B-AS1', 'UBL4B', 'CLEC1B', 'DPYSL4', 'LDHAL6A', 'PRUNE2', 'LINC00200', 'BRME1', 'FAM186B', 'VWA5B1', 'RARRES1', 'LINC01108'], ['SLC1A2-AS1', 'MIR130AHG', 'HEATR4', 'SLC49A3', 'OR6C6', 'SLC4A9', 'IGKV1D-13', 'ACTL7B', 'LINC01823', 'MIPOL1', 'AMPD1', 'IGKV2D-30', 'SLC16A14', 'DEPTOR-AS1', 'EDNRB-AS1', 'H3C12', 'LINC01990', 'ATP8A1-DT', 'TGFB2-AS1'], ['NLRP6', 'PRSS45P', 'NAALADL2', 'VSTM1', 'MYLK3', 'FOXI1', 'PCDHGA3', 'VWA7', 'HDHD5-AS1', 'LINC03021_ENSG00000254319', 'LINC01579', 'IGHV1-14', 'HCG22', 'LINC02055', 'UNC79', 'RNF217-AS1', 'C1orf50-AS1', 'GYS2'], ['CASC9', 'CCDC28A-AS1', 'TRPM1', 'CYP2S1', 'TMPRSS3', 'THTPA', 'GCNT3', 'FREY1', 'RHOXF1-AS1', 'NHS', 'IGHV7-4-1', 'SLITRK5', 'IGLV5-45', 'TRMT9B', 'CFAP57', 'RNF112', 'LINC00654'], ['ASIC3', 'SLC22A1', 'BHLHE22', 'LIF', 'S100A16', 'CT69', 'TRAV29DV5', 'C10orf71', 'TTLL7', 'MS4A4E', 'DNMBP-AS1', 'EDAR'], ['FAM182A', 'PACRG', 'NKX6-1', 'ACTA2-AS1', 'TAS2R39', 'CHRNG', 'LINC02660', 'CDH23'], ['TEKTIP1', 'ASGR2', 'IGKV2-26', 'LINC02057', 'GOLGA8H', 'LRRC49'], ['CYP2C8', 'PELP1-DT', 'LINC01301', 'CBY3', 'PTGR1'], ['KCNH6', 'LINC01980', 'DLG1-AS1', 'IQSEC2', 'LPAR4'], ['MYO3A', 'HSD17B2-AS1', 'DUOX2', 'LINC01115_ENSG00000237667'], ['FCN3', 'PCDHB4', 'S100A5'], ['USP43', 'IGFBP2', 'CNTNAP3'], ['NPM2', 'RHBDF1'], ['STXBP6', 'SERTAD3-AS1']]

In [17]:

len(communities)

len(communities)

Out[17]:

18

In [18]:

import pickle
# Save the separated_communities list as a pkl file
file_path = '/ReCoDE-Gene-Network-Analysis/data/other/separated_communities.pkl'
with open(file_path, 'wb') as file:
    pickle.dump(separated_communities, file)

import pickle # Save the separated_communities list as a pkl file file_path = '/ReCoDE-Gene-Network-Analysis/data/other/separated_communities.pkl' with open(file_path, 'wb') as file: pickle.dump(separated_communities, file)

Step 6: Investigate Chosen Community/Sub-Network¶

In [19]:

# Choose the index of the community you want to visualise
community_index = 0  # Change this to the index of the community you want to visualise

# Get the nodes in the selected community
selected_community = list(communities[community_index])

# Create a subgraph containing only the nodes and edges within the selected community
subgraph = G.subgraph(selected_community)

# Choose the index of the community you want to visualise community_index = 0 # Change this to the index of the community you want to visualise # Get the nodes in the selected community selected_community = list(communities[community_index]) # Create a subgraph containing only the nodes and edges within the selected community subgraph = G.subgraph(selected_community)

In [20]:

# Assuming subgraph is already defined
num_nodes = subgraph.number_of_nodes()
print(f"The number of nodes in the subgraph is: {num_nodes}")

# Assuming subgraph is already defined num_nodes = subgraph.number_of_nodes() print(f"The number of nodes in the subgraph is: {num_nodes}")

The number of nodes in the subgraph is: 70

Step 7: Visualise the Community/Sub-Network¶

In [21]:

# Visualise the subgraph
pos = nx.spring_layout(subgraph, k=0.8, iterations=20)  # You can use different layout algorithms if needed
plt.figure(figsize=(14, 12))
nx.draw(subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8)
plt.title('Community Visualisation')
plt.show()

# Visualise the subgraph pos = nx.spring_layout(subgraph, k=0.8, iterations=20) # You can use different layout algorithms if needed plt.figure(figsize=(14, 12)) nx.draw(subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8) plt.title('Community Visualisation') plt.show()

In [ ]:

Play around with different layouts and see how the visualisation is affected. For example, there is circular_layout. Check out https://networkx.org/documentation/stable/tutorial.html#drawing-graphs for more information.

In [22]:

# Visualise the subgraph
pos = nx.circular_layout(subgraph)  # You can use different layout algorithms if needed
plt.figure(figsize=(14, 12))
nx.draw(subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8)
plt.title('Community Visualisation')
plt.show()

# Visualise the subgraph pos = nx.circular_layout(subgraph) # You can use different layout algorithms if needed plt.figure(figsize=(14, 12)) nx.draw(subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8) plt.title('Community Visualisation') plt.show()

As can be seen here, the circular layout is not really suitable due to the high number of genes within the sub-network that have high density of edges.

Since the subnetwork itself is too large to visualise, we shall visualise a random sample of the subnetwork.

In [23]:

# Select 10 random nodes from the original subgraph
selected_nodes = random.sample(subgraph.nodes(), 10)

# Create a new subgraph containing only the selected nodes and their neighbors
reduced_subgraph = subgraph.subgraph(selected_nodes)

# Select 10 random nodes from the original subgraph selected_nodes = random.sample(subgraph.nodes(), 10) # Create a new subgraph containing only the selected nodes and their neighbors reduced_subgraph = subgraph.subgraph(selected_nodes)

In [24]:

# Visualise the subgraph
pos = nx.circular_layout(reduced_subgraph)  # You can use different layout algorithms if needed
plt.figure(figsize=(14, 12))
nx.draw(reduced_subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8)
plt.title('Community Visualisation')
plt.show()

# Visualise the subgraph pos = nx.circular_layout(reduced_subgraph) # You can use different layout algorithms if needed plt.figure(figsize=(14, 12)) nx.draw(reduced_subgraph, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8) plt.title('Community Visualisation') plt.show()

Try out a different visualisation technique with the randomly sampled subnetwork

In [25]:

# Visualise the subgraph
pos = nx.spectral_layout(reduced_subgraph)  # You can use different layout algorithms if needed
plt.figure(figsize=(14, 12))
nx.draw(reduced_subgraph, pos, with_labels=True, node_color='skyblue', node_size=1000, edge_color='gray', linewidths=0.1, font_size=10)
plt.title('Community Visualisation')
plt.show()

# Visualise the subgraph pos = nx.spectral_layout(reduced_subgraph) # You can use different layout algorithms if needed plt.figure(figsize=(14, 12)) nx.draw(reduced_subgraph, pos, with_labels=True, node_color='skyblue', node_size=1000, edge_color='gray', linewidths=0.1, font_size=10) plt.title('Community Visualisation') plt.show()

In [ ]:

In [ ]:

External Reading Links:

• WGCNA package: https://web.archive.org/web/20230323144343/horvath.genetics.ucla.edu/html/CoexpressionNetwork/Rpackages/WGCNA/
• WGCNA paper: https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-9-559
• Correlation analysis: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5079093/
• Quick introduction page to correlations in statistics: https://www.jmp.com/en_gb/statistics-knowledge-portal/what-is-correlation.html

Exercise Questions:

1. What is a gene co-expression network, and why is it important in understanding biological systems?
2. Explain the concept of Pearson correlation and its use in gene expression analysis.
3. What other correlation measures could be used?
4. Why do we convert a correlation matrix to a distance matrix in hierarchical clustering?
5. What other distance measures could be used?
6. 6. What is hierarchical clustering, and how is it applied in the context of gene co-expression networks?
7. Are there other community-based algorithms that could be used instead?
8. Show a worked through example testing different correlation measures, distance measures and community algorithms and see how this affects the networks produced.

Answers:

1. A gene co-expression network is a type of biological network where nodes represent genes and edges represent significant co-expression relationships between them. These networks are important because they help identify groups of genes (modules) that are co-expressed under various conditions, which can reveal functional relationships and regulatory mechanisms within the biological system. Understanding these networks can lead to insights into gene functions, interactions, and their roles in diseases.
2. Pearson correlation is a measure of the linear relationship between two variables, providing a value between -1 and 1. In gene expression analysis, Pearson correlation is used to quantify the degree to which the expression levels of two genes vary together across different samples or conditions. A value close to 1 indicates strong positive correlation, -1 indicates strong negative correlation, and 0 indicates no linear correlation. This measure helps identify gene pairs that might be co-regulated or involved in the same biological processes.
3. Spearman Rank Correlation measures the strength and direction of the monotonic relationship between two ranked variables. It is useful for ordinal data or when the relationship isn't linear. Kendall Tau Correlation measures the association between two ranked variables. It is suitable for small sample sizes or data with many tied ranks.
4. We convert a correlation matrix to a distance matrix because hierarchical clustering algorithms require a measure of dissimilarity between pairs of genes. The distance matrix represents this dissimilarity, with smaller values indicating more similar (correlated) gene expression profiles. This conversion allows the clustering algorithm to group similar genes together based on their expression patterns, facilitating the identification of co-expressed gene modules.
5. Euclidean Distance is the straight-line distance between two points in Euclidean space. Manhattan Distance is the sum of absolute differences between the coordinates of two points. Minkowski Distance is a generalisation that includes both Euclidean and Manhattan distances. By providing a comprehensive way to quantify relationships between objects, distance matrices play a fundamental role in data analysis, pattern recognition, and various scientific research fields.
6. Hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. It is applied in gene co-expression networks to group genes with similar expression patterns. The process starts with each gene as its own cluster and iteratively merges the most similar clusters based on their distance, forming a tree-like structure called a dendrogram. This helps visualise the relationships between genes and identify clusters of co-expressed genes.
7. The Louvain method is an efficient algorithm for community detection that optimises modularity. The Girvan-Newman algorithm detects communities by progressively removing edges with the highest betweenness centrality.

Question 8:

In [26]:

#Calculate correlation using Spearman Rank Correlation:
correlation_matrix2 = datExpr.corr(method = 'spearman')

#Calculate correlation using Spearman Rank Correlation: correlation_matrix2 = datExpr.corr(method = 'spearman')

In [27]:

correlation_matrix2

correlation_matrix2

Out[27]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
ISG15	1.000000	0.016319	-0.056208	0.686548	-0.165674	-0.037170	0.049862	-0.069807	0.222848	-0.075307	...	0.369104	0.486957	0.165674	0.165674	0.105429	0.165674	0.135552	0.266461	0.116547	0.203655
LINC01342	0.016319	1.000000	0.452741	-0.237069	-0.062810	-0.090737	0.452741	-0.090737	0.261696	0.722315	...	0.321733	0.320931	-0.062810	-0.062810	0.659505	-0.062810	-0.062810	-0.134016	0.140551	-0.009074
TTLL10-AS1	-0.056208	0.452741	1.000000	-0.149824	-0.062810	-0.090737	-0.090737	-0.090737	-0.153188	-0.062810	...	0.359584	0.269256	-0.062810	-0.062810	0.722315	-0.062810	-0.062810	-0.134016	-0.192238	-0.389263
TNFRSF18	0.686548	-0.237069	-0.149824	1.000000	-0.136595	0.265847	-0.063493	-0.040654	-0.004319	-0.273190	...	0.294203	0.108656	0.288367	0.288367	-0.045532	0.288367	0.166950	0.193963	0.016433	0.368349
CALML6	-0.165674	-0.062810	-0.062810	-0.136595	1.000000	-0.062810	-0.062810	-0.062810	-0.106040	-0.043478	...	-0.078603	0.195797	-0.043478	-0.043478	-0.043478	-0.043478	-0.043478	-0.092769	-0.165710	-0.165819
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TMEM255A	0.165674	-0.062810	-0.062810	0.288367	-0.043478	-0.062810	-0.062810	-0.062810	-0.106040	-0.043478	...	-0.078603	0.165674	1.000000	1.000000	-0.043478	1.000000	-0.043478	-0.092769	0.286227	0.316563
SMIM10L2B-AS1	0.135552	-0.062810	-0.062810	0.166950	-0.043478	-0.062810	0.722315	-0.062810	-0.106040	-0.043478	...	-0.078603	0.015061	-0.043478	-0.043478	-0.043478	-0.043478	1.000000	0.487035	0.135581	0.256265
IL9R_ENSG00000124334	0.266461	-0.134016	-0.134016	0.193963	-0.092769	0.267335	0.302235	-0.134016	-0.008485	-0.092769	...	-0.167714	0.181434	-0.092769	-0.092769	-0.092769	-0.092769	0.487035	1.000000	-0.108148	0.060307
DDX3Y	0.116547	0.140551	-0.192238	0.016433	-0.165710	-0.246645	0.279289	-0.265687	0.304952	0.256098	...	-0.395663	0.203523	0.286227	0.286227	-0.075323	0.286227	0.135581	-0.108148	1.000000	0.829598
EIF1AY	0.203655	-0.009074	-0.389263	0.368349	-0.165819	-0.068960	0.328469	-0.286730	0.251229	0.195968	...	-0.411819	0.026110	0.316563	0.316563	-0.226116	0.316563	0.256265	0.060307	0.829598	1.000000

1000 rows × 1000 columns

Calculate distance matrix using Minkowski Distance

Convert correlation matrix to distance matrix Here, we use 1 - correlation as the distance measure by first calculating the dissimilarity

In [28]:

distance_matrix2 = 1 - correlation_matrix2

# Calculate the Minkowski distance (p = 2 for Euclidean, p = 1 for Manhattan, etc.)
p = 3  # You can change this to any value of p
minkowski_distances = pdist(distance_matrix2, metric='minkowski', p=p)

# Convert back to square form
distance_matrix_minkowski = squareform(minkowski_distances)

distance_matrix2 = 1 - correlation_matrix2 # Calculate the Minkowski distance (p = 2 for Euclidean, p = 1 for Manhattan, etc.) p = 3 # You can change this to any value of p minkowski_distances = pdist(distance_matrix2, metric='minkowski', p=p) # Convert back to square form distance_matrix_minkowski = squareform(minkowski_distances)

In [29]:

distance_matrix_minkowski

distance_matrix_minkowski

Out[29]:

array([[0.        , 4.97451632, 5.31047871, ..., 4.11670602, 4.41095818,
        4.07169558],
       [4.97451632, 0.        , 2.81633536, ..., 3.94219913, 3.39496526,
        4.15888346],
       [5.31047871, 2.81633536, 0.        , ..., 3.8634609 , 3.85574122,
        4.57033685],
       ...,
       [4.11670602, 3.94219913, 3.8634609 , ..., 0.        , 3.54310329,
        3.11503694],
       [4.41095818, 3.39496526, 3.85574122, ..., 3.54310329, 0.        ,
        1.79073525],
       [4.07169558, 4.15888346, 4.57033685, ..., 3.11503694, 1.79073525,
        0.        ]])

In [30]:

# Convert back to DataFrame to keep row and column names
#In order to do that save the row and column names from the original correlation matrix first:

row_labels = correlation_matrix.index
column_labels = correlation_matrix.columns

#Convert the distance matrix into a dataframe
distance_df = pd.DataFrame(distance_matrix_minkowski, index=row_labels, columns=column_labels)

# Convert back to DataFrame to keep row and column names #In order to do that save the row and column names from the original correlation matrix first: row_labels = correlation_matrix.index column_labels = correlation_matrix.columns #Convert the distance matrix into a dataframe distance_df = pd.DataFrame(distance_matrix_minkowski, index=row_labels, columns=column_labels)

In [31]:

distance_df

distance_df

Out[31]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
ISG15	0.000000	4.974516	5.310479	2.479338	5.256966	5.137140	4.833509	6.154665	4.101156	5.488098	...	3.468319	3.099291	4.518263	4.518263	4.631243	4.518263	4.700795	4.116706	4.410958	4.071696
LINC01342	4.974516	0.000000	2.816335	5.643094	4.218496	4.195265	3.144677	4.192129	3.099887	2.302618	...	3.323716	4.142144	5.375076	5.375076	2.521129	5.375076	4.265176	3.942199	3.394965	4.158883
TTLL10-AS1	5.310479	2.816335	0.000000	5.641991	4.085150	3.976405	3.911277	3.799220	3.834896	3.974338	...	3.049130	4.647630	5.344209	5.344209	1.850177	5.344209	4.147613	3.863461	3.855741	4.570337
TNFRSF18	2.479338	5.643094	5.641991	0.000000	5.508208	4.336978	4.984989	5.608852	4.892775	5.900174	...	3.693057	4.861216	4.060531	4.060531	5.197886	4.060531	4.323955	3.887995	4.615055	3.413775
CALML6	5.256966	4.218496	4.085150	5.508208	0.000000	4.506604	4.367332	4.538077	4.231430	4.442941	...	4.214099	4.341695	5.488562	5.488562	4.288198	5.488562	4.537409	4.287737	4.430332	4.692939
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TMEM255A	4.518263	5.375076	5.344209	4.060531	5.488562	5.278605	5.328074	5.496537	5.339846	5.455101	...	5.181272	4.935519	0.000000	0.000000	5.318906	0.000000	5.310234	5.211184	3.732318	3.549149
SMIM10L2B-AS1	4.700795	4.265176	4.147613	4.323955	4.537409	3.970086	2.314571	3.959092	4.193764	4.310500	...	4.015744	5.423327	5.310234	5.310234	4.340555	5.310234	0.000000	2.426073	3.434198	3.095993
IL9R_ENSG00000124334	4.116706	3.942199	3.863461	3.887995	4.287737	2.609322	2.953918	3.696751	3.531675	3.992939	...	3.640487	4.822124	5.211184	5.211184	4.059895	5.211184	2.426073	0.000000	3.543103	3.115037
DDX3Y	4.410958	3.394965	3.855741	4.615055	4.430332	4.203337	2.995581	3.928682	2.754223	3.155120	...	4.137625	4.486492	3.732318	3.732318	4.001664	3.732318	3.434198	3.543103	0.000000	1.790735
EIF1AY	4.071696	4.158883	4.570337	3.413775	4.692939	3.711069	3.040494	3.978252	3.405516	3.697280	...	4.162647	5.164845	3.549149	3.549149	4.624298	3.549149	3.095993	3.115037	1.790735	0.000000

1000 rows × 1000 columns

In [32]:

#The linkage function is used to perform hierarchical clustering on the distance matrix. 
linkage_matrix2 = sch.linkage(distance_df, method='average')

# Plot the dendrogram
plt.figure(figsize=(10, 6))
dendrogram = sch.dendrogram(linkage_matrix2)
plt.title('Hierarchical Clustering Dendrogram')
plt.xlabel('Sample Index')
plt.ylabel('Distance')
plt.show()

#The linkage function is used to perform hierarchical clustering on the distance matrix. linkage_matrix2 = sch.linkage(distance_df, method='average') # Plot the dendrogram plt.figure(figsize=(10, 6)) dendrogram = sch.dendrogram(linkage_matrix2) plt.title('Hierarchical Clustering Dendrogram') plt.xlabel('Sample Index') plt.ylabel('Distance') plt.show()

/tmp/ipykernel_128889/2932722225.py:2: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix
  linkage_matrix2 = sch.linkage(distance_df, method='average')

In [33]:

# Define threshold for significant edges (you can adjust this based on your requirement)
threshold = 0.7

# Threshold the correlation matrix to determine significant edges
significant_edges2 = correlation_matrix2 > threshold

# Define threshold for significant edges (you can adjust this based on your requirement) threshold = 0.7 # Threshold the correlation matrix to determine significant edges significant_edges2 = correlation_matrix2 > threshold

In [34]:

significant_edges2

significant_edges2

Out[34]:

	ISG15	LINC01342	TTLL10-AS1	TNFRSF18	CALML6	CHD5	ICMT-DT	MIR34AHG	RBP7	MTOR-AS1	...	FRMPD3	TSC22D3	KLHL13	AKAP14	RHOXF1-AS1	TMEM255A	SMIM10L2B-AS1	IL9R_ENSG00000124334	DDX3Y	EIF1AY
ISG15	True	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
LINC01342	False	True	False	False	False	False	False	False	False	True	...	False	False	False	False	False	False	False	False	False	False
TTLL10-AS1	False	False	True	False	False	False	False	False	False	False	...	False	False	False	False	True	False	False	False	False	False
TNFRSF18	False	False	False	True	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
CALML6	False	False	False	False	True	False	False	False	False	False	...	False	False	False	False	False	False	False	False	False	False
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TMEM255A	False	False	False	False	False	False	False	False	False	False	...	False	False	True	True	False	True	False	False	False	False
SMIM10L2B-AS1	False	False	False	False	False	False	True	False	False	False	...	False	False	False	False	False	False	True	False	False	False
IL9R_ENSG00000124334	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	True	False	False
DDX3Y	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	True	True
EIF1AY	False	False	False	False	False	False	False	False	False	False	...	False	False	False	False	False	False	False	False	True	True

1000 rows × 1000 columns

In [35]:

#networkx is a python library designed for network analysis.
# Construct the network from significant edges.
G2 = nx.Graph()

# Loop through significant edges and add edges to the graph
for i in range(significant_edges2.shape[0]):
    for j in range(significant_edges2.shape[1]):
        if significant_edges2.values[i, j]:
            gene1 = significant_edges2.index[i]
            gene2 = significant_edges2.columns[j]
            
            # Find the position of gene1 and gene2 in the correlation matrix
            i_corr = np.where(correlation_matrix2.index == gene1)[0][0]
            j_corr = np.where(correlation_matrix2.columns == gene2)[0][0]
            
            # Add the edge to the graph
            G2.add_edge(gene1, gene2, weight=correlation_matrix2.iloc[i_corr, j_corr])

# Display the number of nodes and edges in the graph
print("Number of nodes:", G2.number_of_nodes())
print("Number of edges:", G2.number_of_edges())

#networkx is a python library designed for network analysis. # Construct the network from significant edges. G2 = nx.Graph() # Loop through significant edges and add edges to the graph for i in range(significant_edges2.shape[0]): for j in range(significant_edges2.shape[1]): if significant_edges2.values[i, j]: gene1 = significant_edges2.index[i] gene2 = significant_edges2.columns[j] # Find the position of gene1 and gene2 in the correlation matrix i_corr = np.where(correlation_matrix2.index == gene1)[0][0] j_corr = np.where(correlation_matrix2.columns == gene2)[0][0] # Add the edge to the graph G2.add_edge(gene1, gene2, weight=correlation_matrix2.iloc[i_corr, j_corr]) # Display the number of nodes and edges in the graph print("Number of nodes:", G2.number_of_nodes()) print("Number of edges:", G2.number_of_edges())

Number of nodes: 1000
Number of edges: 30389

Analyse the network: For example, you can identify clusters/modules using community detection algorithms Connected_components is a quick and simple community detection algorithm. While this method may not be as sophisticated as algorithms like Louvain or Girvan-Newman, it can provide a basic partitioning of the graph into communities.

In [36]:

communities2 = list(nx.connected_components(G2))

communities2 = list(nx.connected_components(G2))

In [37]:

communities2

communities2

Out[37]:

[{'ABALON',
  'ACP5',
  'ACSL3-AS1',
  'ACSM3',
  'ACTA2-AS1',
  'ACTG1',
  'ACTN3',
  'ACVR2B-AS1',
  'ADAM19',
  'ADAMTS13',
  'ADARB2',
  'ADGRG3',
  'AFF3',
  'AHSP',
  'AIFM3',
  'AIM2',
  'AKAP13-AS1',
  'AKAP14',
  'ALDH1A1',
  'ALDH1L2',
  'ALDH8A1',
  'ALKAL2',
  'AMOTL1',
  'ANKRD28',
  'ANKRD29',
  'ANKRD44-DT',
  'ANKRD61',
  'ANO1',
  'ANO8',
  'ANXA1',
  'APOE',
  'AREG',
  'ARHGAP15',
  'ARHGAP17',
  'ARHGAP22',
  'ARHGAP23',
  'ARHGAP29',
  'ARHGAP39',
  'ARHGEF10L',
  'ARHGEF39',
  'ARID5B',
  'ARL4A',
  'ARL4C',
  'ARPP21',
  'ASGR1',
  'ASGR2',
  'ASIC3',
  'ASPN',
  'ATF7IP2',
  'ATP1A3',
  'ATP1B3',
  'ATP2B1-AS1',
  'AVP',
  'AZU1',
  'BANK1',
  'BASP1',
  'BAZ2B',
  'BCAR4',
  'BCL11B',
  'BCL2A1',
  'BCL7A',
  'BEX1',
  'BHLHE22',
  'BHLHE40',
  'BMP3',
  'BORCS5',
  'BRME1',
  'BSN',
  'BTG1-DT',
  'C10orf105',
  'C10orf71',
  'C12orf71',
  'C15orf48',
  'C16orf74',
  'C18orf63',
  'C19orf67',
  'C1QTNF7',
  'C1orf131',
  'C1orf162',
  'C1orf50-AS1',
  'C1orf56',
  'C20orf144',
  'C21orf62',
  'C7orf50',
  'CA1',
  'CACTIN-AS1',
  'CADM4',
  'CALCA',
  'CALHM6',
  'CALML6',
  'CAMK2D',
  'CAPN14',
  'CASC9',
  'CAVIN2',
  'CAVIN3',
  'CC2D2B',
  'CCDC110',
  'CCDC28A-AS1',
  'CCK',
  'CCL22',
  'CCL3',
  'CCL3L3',
  'CCL4',
  'CCL4L2',
  'CCL5',
  'CCL7',
  'CCN1',
  'CCNA1',
  'CCND2',
  'CCR7',
  'CD109',
  'CD19',
  'CD2',
  'CD22',
  'CD24',
  'CD2AP-DT',
  'CD3D',
  'CD3G',
  'CD52',
  'CD69',
  'CD70',
  'CD72',
  'CD79B',
  'CD83',
  'CDC42EP1',
  'CDCA7L',
  'CDH13-AS2',
  'CDH23',
  'CDH24',
  'CDH6',
  'CEACAM1',
  'CELSR2',
  'CELSR3',
  'CEP290',
  'CEP295NL',
  'CERCAM',
  'CFAP126',
  'CFAP141',
  'CFAP157',
  'CFAP418-AS1',
  'CFAP57',
  'CFAP99',
  'CHD5',
  'CHML',
  'CHMP1B',
  'CHMP1B-AS1',
  'CHRNG',
  'CITED2',
  'CKS2',
  'CLDN11',
  'CLEC10A',
  'CLEC1A',
  'CLEC1B',
  'CLEC2D',
  'CLGN',
  'CLU',
  'CMSS1',
  'CMTM5',
  'CNKSR3',
  'CNTNAP2',
  'CNTNAP3',
  'COL11A2',
  'COL19A1',
  'COLEC12',
  'COPDA1',
  'COQ7',
  'CPLANE1-AS1',
  'CREM',
  'CRIP1',
  'CRIP2',
  'CSRP2',
  'CST7',
  'CT69',
  'CTAGE9',
  'CUX2',
  'CXCL10',
  'CXCL2',
  'CXCL3',
  'CXCL8',
  'CXCR1',
  'CYB561A3',
  'CYP26C1',
  'CYP2D6',
  'CYP2S1',
  'CYP2U1-AS1',
  'CYTOR',
  'CYYR1',
  'DAAM1',
  'DAGLA',
  'DBH-AS1',
  'DBNDD1',
  'DBX2',
  'DCTN1-AS1',
  'DENND6A-AS1',
  'DEPDC7',
  'DGKD',
  'DINOL',
  'DIO3',
  'DLG1-AS1',
  'DLGAP2',
  'DNAJB1',
  'DNAJC12',
  'DNAJC9-AS1_ENSG00000236756',
  'DNMBP-AS1',
  'DOCK8-AS1',
  'DPYD-IT1',
  'DPYSL3',
  'DPYSL4',
  'DSG2',
  'DTNA',
  'DUOX2',
  'DUSP1',
  'DUSP2',
  'DUSP4',
  'DYNLRB2-AS1',
  'EAF2',
  'ECEL1',
  'ECM1',
  'EDAR',
  'EGR1',
  'EGR3',
  'ELF3',
  'ELFN1-AS1',
  'EML1',
  'EPB41L1',
  'EPHA2',
  'EPHB2',
  'EPHB4',
  'EPSTI1',
  'EQTN',
  'ERCC2',
  'ESCO2',
  'ETV5',
  'FABP5',
  'FAM106A',
  'FAM111A',
  'FAM111B',
  'FAM174A-DT',
  'FAM182A',
  'FAM186B',
  'FAM200B',
  'FAM20C',
  'FAM30A',
  'FBLIM1',
  'FBXO22',
  'FCER1G',
  'FCER2',
  'FCHSD2',
  'FCN3',
  'FCRL1',
  'FCRL2',
  'FCRL5',
  'FCRLA',
  'FGFBP2',
  'FMOD',
  'FNDC5',
  'FOS',
  'FOSB',
  'FOXD3',
  'FOXI1',
  'FOXP1-AS1',
  'FRA10AC1',
  'FREY1',
  'FRMPD3',
  'FSTL1',
  'FTH1',
  'GABARAPL1',
  'GABRB2',
  'GADD45B',
  'GAPDH',
  'GAPT',
  'GARIN4',
  'GAS5-AS1',
  'GBP1',
  'GBP2',
  'GBP4',
  'GBP5',
  'GCM1',
  'GCNT3',
  'GIHCG',
  'GIMAP7',
  'GJB6',
  'GJC2',
  'GJD3',
  'GLA',
  'GLP2R',
  'GNG12',
  'GNLY',
  'GOLGA8H',
  'GOLGA8R',
  'GORAB-AS1',
  'GP1BB',
  'GP9',
  'GPR137C',
  'GPR183',
  'GPR3',
  'GPRC5A',
  'GRB10',
  'GRIN2B',
  'GSTA1',
  'GUCD1',
  'GYS2',
  'GZMA',
  'GZMB',
  'GZMH',
  'GZMM',
  'H1-10',
  'H1-3',
  'H2AC6',
  'H3-3A-DT',
  'H3C3',
  'H3C8',
  'HBD',
  'HCAR2',
  'HCCS-DT',
  'HCG22',
  'HCG9',
  'HCN3',
  'HCST',
  'HDAC9',
  'HDHD5-AS1',
  'HELQ',
  'HELZ-AS1',
  'HERC5',
  'HES1',
  'HEXIM1',
  'HEY1',
  'HGF',
  'HIP1R',
  'HLA-DMB',
  'HLA-DOB',
  'HOPX',
  'HOXA5',
  'HSD17B2-AS1',
  'HSPA1A',
  'HSPA1B',
  'HSPA5-DT',
  'HSPA6',
  'HSPB1',
  'HSPH1',
  'HYDIN',
  'ICA1-AS1',
  'ICMT-DT',
  'ICOSLG',
  'ID1',
  'ID2',
  'ID3',
  'IFI30',
  'IFIT2',
  'IFRD1',
  'IGFBP2',
  'IGHA1',
  'IGHA2',
  'IGHD',
  'IGHE',
  'IGHG1',
  'IGHG3',
  'IGHG4',
  'IGHM',
  'IGHV1-14',
  'IGHV1-18',
  'IGHV1-69',
  'IGHV2-5',
  'IGHV2-70',
  'IGHV3-11',
  'IGHV3-32',
  'IGHV3-69-1',
  'IGHV3-72',
  'IGHV3-73',
  'IGHV4-34',
  'IGHV7-4-1',
  'IGKC',
  'IGKV1-6',
  'IGKV1-9',
  'IGKV1D-39',
  'IGKV2-26',
  'IGKV2D-29',
  'IGKV3D-11',
  'IGKV4-1',
  'IGLC1',
  'IGLC2',
  'IGLC3',
  'IGLC4',
  'IGLC6',
  'IGLC7',
  'IGLV1-44',
  'IGLV2-18',
  'IGLV3-10',
  'IGLV3-16',
  'IGLV3-9',
  'IGLV5-37',
  'IGLV5-45',
  'IL11',
  'IL32',
  'IL4R',
  'IL7R',
  'IL9R_ENSG00000124334',
  'ILF3-DT',
  'INKA2-AS1',
  'IQCA1',
  'IQSEC2',
  'IRF4',
  'IRF8',
  'IRS2',
  'ISG15',
  'ITGB5',
  'ITPR1',
  'JAG2',
  'JARID2-AS1',
  'JCHAIN',
  'JMY',
  'JUN',
  'JUNB',
  'KBTBD11-AS1',
  'KCNE3',
  'KCNH6',
  'KCNJ1',
  'KCNQ1OT1',
  'KCNQ4',
  'KLF10',
  'KLF2',
  'KLF3-AS1',
  'KLF4',
  'KLHL10',
  'KLHL13',
  'KLHL22',
  'KLHL32',
  'KLRB1',
  'KLRD1',
  'KMT2E-AS1',
  'KRT2',
  'LAMA2',
  'LAMP5',
  'LANCL3',
  'LAPTM4A-DT',
  'LARP7',
  'LCN2',
  'LCNL1',
  'LDHAL6A',
  'LGALS1',
  'LGALS3',
  'LGALS9C',
  'LGALSL-DT',
  'LIF',
  'LILRA1',
  'LILRA6',
  'LIM2',
  'LIN28A',
  'LINC00106_ENSG00000236871',
  'LINC00200',
  'LINC00310',
  'LINC00520',
  'LINC00640',
  'LINC00654',
  'LINC00964',
  'LINC00997',
  'LINC01050',
  'LINC01104',
  'LINC01108',
  'LINC01115_ENSG00000237667',
  'LINC01133',
  'LINC01260',
  'LINC01284',
  'LINC01342',
  'LINC01354',
  'LINC01375',
  'LINC01389',
  'LINC01503',
  'LINC01579',
  'LINC01764',
  'LINC01781',
  'LINC01801',
  'LINC01832',
  'LINC01891',
  'LINC01962',
  'LINC01980',
  'LINC01986',
  'LINC01991',
  'LINC02029',
  'LINC02055',
  'LINC02057',
  'LINC02076',
  'LINC02175',
  'LINC02267',
  'LINC02285',
  'LINC02348',
  'LINC02397',
  'LINC02540',
  'LINC02551',
  'LINC02569',
  'LINC02595',
  'LINC02615',
  'LINC02631',
  'LINC02660',
  'LINC02679',
  'LINC02842',
  'LINC02851',
  'LINC02880',
  'LINC02968_ENSG00000223511',
  'LINC03019',
  'LINC03021_ENSG00000254319',
  'LINC03040',
  'LINC03065',
  'LINC03080',
  'LIX1L-AS1',
  'LMNA',
  'LNCOC1',
  'LNP1',
  'LOH12CR2',
  'LPAR4',
  'LPP',
  'LRRC49',
  'LRRC66',
  'LRRC75B',
  'LRRN2',
  'LRRTM4',
  'LSAMP',
  'LST1',
  'LTB',
  'LY6G6C',
  'LY86',
  'LY9',
  'LYPD5',
  'LYZ',
  'MAD2L1-DT',
  'MAG',
  'MANSC1',
  'MAP3K6',
  'MAP3K8',
  'MAP7D2',
  'MAPK12',
  'MARCHF1',
  'MARCHF3',
  'MARCKS',
  'MAS1',
  'MBD5',
  'MCM10',
  'MEG3',
  'METTL8',
  'MEX3B',
  'MGAM',
  'MGP',
  'MIA2-AS1',
  'MINDY2-DT',
  'MIR155HG',
  'MIR23AHG',
  'MIR34AHG',
  'MIR4432HG',
  'MKI67',
  'MMP2-AS1',
  'MMP28',
  'MOBP',
  'MOCS1',
  'MROH8',
  'MS4A1',
  'MS4A4E',
  'MSMP',
  'MSS51',
  'MT2A',
  'MTFR2',
  'MTOR-AS1',
  'MTRFR',
  'MTTP',
  'MTUS2-AS1',
  'MUCL3',
  'MX1',
  'MX2',
  'MYADM',
  'MYC',
  'MYL3',
  'MYL6B-AS1',
  'MYLK3',
  'MYO10',
  'MYO3A',
  'MYO3B',
  'MYO7B',
  'MYOZ3',
  'MYZAP',
  'MZB1',
  'MZF1-AS1',
  'NAALADL2',
  'NAF1',
  'NEIL1',
  'NFE2',
  'NFKB1',
  'NFKBID',
  'NGFR',
  'NHLH1',
  'NHS',
  'NIBAN3',
  'NIM1K',
  'NKD2',
  'NKG7',
  'NKX6-1',
  'NKX6-2',
  'NKX6-3',
  'NLRP12',
  'NLRP6',
  'NME4',
  'NPM2',
  'NR2E3',
  'NR4A1',
  'NR4A2',
  'NR4A3',
  'NRDE2',
  'NREP',
  'NRGN',
  'NTN4',
  'NUAK2',
  'ODAD1',
  'ODAD3',
  'OMD',
  'OPA1-AS1',
  'OR2A1-AS1',
  'OR2AK2',
  'OR2B11',
  'OR2T2',
  'OR52N4',
  'OR56B1',
  'OSBPL10',
  'OXCT1-AS1',
  'OXTR',
  'P2RX5',
  'P2RY1',
  'P2RY13',
  'PACRG',
  'PALM',
  'PAPPA-AS1',
  'PCDH9',
  'PCDHB4',
  'PCDHGA3',
  'PCSK1',
  'PCSK6',
  'PDF',
  'PDK4-AS1',
  'PEG10',
  'PF4',
  'PF4V1',
  'PGAM2',
  'PGM2L1',
  'PHACTR1',
  'PHACTR3',
  'PIGY-DT',
  'PITPNM2-AS1',
  'PLCG2',
  'PLEK',
  'PLEKHA4',
  'PLPP5',
  'PLSCR2',
  'PMAIP1',
  'PNOC',
  'POU3F3',
  'PPBP',
  'PPM1J',
  'PPP1R12A-AS1',
  'PPP1R14A',
  'PPP1R14B-AS1',
  'PPP1R17',
  'PPP1R2C',
  'PPP1R9A-AS1',
  'PRAM1',
  'PRECSIT',
  'PRKD3-DT',
  'PRLR',
  'PROSER2',
  'PRPF19-DT',
  'PRR15',
  'PRRT3-AS1',
  'PRSS45P',
  'PRUNE2',
  'PTCH2',
  'PTGDS',
  'PTGER4',
  'PTGES',
  'PTK6',
  'PTPN6',
  'PTPRD-AS1',
  'PYGL',
  'RAB33B-AS1',
  'RAB6C',
  'RALGPS2',
  'RARRES1',
  'RARRES2',
  'RASSF8',
  'RBFADN',
  'RBP7',
  'REEP1',
  'REG1A',
  'RENO1',
  'RGCC',
  'RGL3',
  'RGPD6',
  'RGS1',
  'RGS18',
  'RGS2',
  'RHBDF1',
  'RHOB',
  'RHOXF1-AS1',
  'RIPOR1',
  'RNASEH2B-AS1',
  'RNF112',
  'RNF182',
  'RNF217-AS1',
  'RNGTT',
  'ROBO3',
  'RP9',
  'RPGR',
  'RPRML',
  'RRAD',
  'RRS1-DT',
  'RSPH1-DT',
  'RXFP1',
  'S100A10',
  'S100A11',
  'S100A16',
  'S100A4',
  'S100A5',
  'S100A8',
  'S100A9',
  'SAMD9L',
  'SAMSN1',
  'SAT1',
  'SCARF2',
  'SCIMP',
  'SCN8A',
  'SCPEP1',
  'SCT',
  'SCUBE3-AS1',
  'SDC2',
  'SEMA3C',
  'SERPINB2',
  'SERPINE3',
  'SERTAD2',
  'SETBP1',
  'SH3RF3',
  'SIRPB1',
  'SKAP1',
  'SLAMF1',
  'SLAMF7',
  'SLC10A5',
  'SLC12A3',
  'SLC17A7',
  'SLC22A1',
  'SLC22A13',
  'SLC25A18',
  'SLC25A37',
  'SLC26A8',
  'SLC28A2',
  'SLC2A4',
  'SLC39A10',
  'SLC3A2',
  'SLC4A3',
  'SLC5A5',
  'SLC6A3',
  'SLFN5',
  'SLITRK5',
  'SMIM10L2B-AS1',
  'SMIM17',
  'SNX22',
  'SNX29',
  'SOX4',
  'SPDYE21',
  'SPIRE2',
  'SPX',
  'SQSTM1',
  'SRGAP3',
  'SRRM5',
  'ST8SIA5',
  'STAG1-DT',
  'STAP2',
  'STAR',
  'STARD6',
  'STON2',
  'STRC',
  'STX1B',
  'TAF1L',
  'TAL1',
  'TAPT1',
  'TAS2R19',
  'TAS2R39',
  'TAT-AS1',
  'TBC1D5',
  'TCF4',
  'TCF7L1',
  'TCL1A',
  'TDRD1',
  'TDRP',
  'TECTA',
  'TEKTIP1',
  'TESC',
  'TEX45',
  'TFAP2A',
  'TFPI2',
  'TGM1',
  'THBS1',
  'THTPA',
  'TIMP3',
  'TKTL2',
  'TLE1',
  'TM4SF1',
  'TMEM107',
  'TMEM176A',
  'TMEM255A',
  'TMEM72-AS1',
  'TMPRSS3',
  'TMSB10',
  'TNFRSF13B',
  'TNFRSF18',
  'TNNC1',
  'TNS2',
  'TOB1',
  'TP53INP1',
  'TP53RK-DT',
  'TRAV29DV5',
  'TRBC1',
  'TRBJ2-4',
  'TRERNA1',
  'TRIM52-AS1',
  'TRIM72',
  'TRMT9B',
  'TRPM1',
  'TSC22D3',
  'TSPAN13',
  'TTC28-AS1',
  'TTLL10-AS1',
  'TTLL7',
  'TTN',
  'TUBA1A',
  'TUBA8',
  'TVP23A',
  'TWIST2',
  'TXNIP',
  'TYMP',
  'TYROBP',
  'UBE2Q2P16',
  'UBL4B',
  'UCP2',
  'UNC79',
  'UPK3A',
  'USP43',
  'VAV3',
  'VIM',
  'VPREB3',
  'VSIG2',
  'VSIR',
  'VSTM1',
  'VSTM4',
  'VWA5B1',
  'VWA7',
  'WAC-AS1',
  'WBP4',
  'WNT3A',
  'WNT5B',
  'XAF1',
  'XCL2',
  'XG',
  'YBX3',
  'ZBTB18',
  'ZBTB20',
  'ZC2HC1B',
  'ZC3H12C',
  'ZCCHC9',
  'ZDHHC11B',
  'ZDHHC17',
  'ZFP28-DT',
  'ZFP36',
  'ZFP36L2',
  'ZMYND12',
  'ZMYND8',
  'ZNF318',
  'ZNF32-AS2',
  'ZNF320',
  'ZNF331',
  'ZNF462',
  'ZNF473CR',
  'ZNF474',
  'ZNF491',
  'ZNF497-AS1',
  'ZNF503',
  'ZNF521',
  'ZNF578',
  'ZNF665',
  'ZNRF3-AS1',
  'ZSCAN10',
  'ZSCAN2-AS1',
  'ZSCAN23'},
 {'PDZK1IP1', 'TFAP2E', 'ZNF697'},
 {'LRRIQ3'},
 {'ACTL7B',
  'AMPD1',
  'ATP8A1-DT',
  'DEPTOR-AS1',
  'EDNRB-AS1',
  'H3C12',
  'HEATR4',
  'IGKV1D-13',
  'IGKV2D-30',
  'LINC01823',
  'LINC01990',
  'MIPOL1',
  'MIR130AHG',
  'OR6C6',
  'SLC16A14',
  'SLC1A2-AS1',
  'SLC49A3',
  'SLC4A9',
  'TGFB2-AS1',
  'TUBB2B'},
 {'XCL1'},
 {'C1orf74'},
 {'EXO1'},
 {'ARNILA'},
 {'DQX1', 'HTR1F', 'SERTAD3-AS1', 'STXBP6', 'ZNF98'},
 {'LINC01857'},
 {'MAP2'},
 {'CHL1-AS2'},
 {'EFHB'},
 {'CTDSPL'},
 {'CDCA5', 'KRBOX1'},
 {'DNASE1L3'},
 {'CFAP20DC', 'MIF-AS1'},
 {'DPPA4'},
 {'SOX2-OT'},
 {'LPP-AS2'},
 {'OSTN'},
 {'ATP13A4'},
 {'SMIM14-DT'},
 {'TSPAN5-DT'},
 {'IL2'},
 {'FGF2'},
 {'AGA-DT'},
 {'RAB3C'},
 {'S100Z'},
 {'CBY3', 'CYP2C8', 'DMXL1-DT', 'ECI1-AS1', 'LINC01301', 'PELP1-DT', 'PTGR1'},
 {'ALDH7A1'},
 {'KCTD16'},
 {'CAGE1'},
 {'H2BC13'},
 {'HLA-DRB5'},
 {'HLA-DQA2'},
 {'LINC01013'},
 {'TRBV14'},
 {'IGHV3-49', 'TRBV28'},
 {'OSR2', 'TONSL'},
 {'CCDC87', 'FOXH1', 'GPHA2', 'HTRA1'},
 {'ZNF252P-AS1'},
 {'STOX1'},
 {'TNKS2-DT'},
 {'KCNIP2'},
 {'HBA1', 'HBA2', 'HBB'},
 {'IRAG1-AS1'},
 {'BDNF-AS'},
 {'TMEM123-DT'},
 {'BACE1-AS'},
 {'PHLDA1-DT'},
 {'IGHV1-3'},
 {'IGHV3-30'},
 {'IGHV4-39'},
 {'IGHV5-51'},
 {'IGHV3-53'},
 {'PIF1'},
 {'ANKRD40CL'},
 {'SMIM5'},
 {'NPTX1'},
 {'MTCL1'},
 {'NETO1-DT'},
 {'RASGRP4'},
 {'ZNF233'},
 {'STK4-DT'},
 {'AATBC'},
 {'S100B'},
 {'IGLV3-19'},
 {'IGLV2-14'},
 {'SERHL2'},
 {'KLHDC7B-DT'},
 {'CLCN4'},
 {'XIST'},
 {'DDX3Y', 'EIF1AY'}]

In [38]:

# Initialise a new graph for community visualisation
community_graph2 = nx.Graph()

# Initialise a new graph for community visualisation community_graph2 = nx.Graph()

In [39]:

# Add edges between communities based on their connectivity
for i, community in enumerate(communities2):
    for node in community:
        community_graph2.add_node(node)
        for neighbor in G2.neighbors(node):
            if neighbor in community:
                community_graph2.add_edge(node, neighbor, weight=G2[node][neighbor]['weight'])

# Add edges between communities based on their connectivity for i, community in enumerate(communities2): for node in community: community_graph2.add_node(node) for neighbor in G2.neighbors(node): if neighbor in community: community_graph2.add_edge(node, neighbor, weight=G2[node][neighbor]['weight'])

In [40]:

# Initialise an empty list to store separated communities
separated_communities = []

# Iterate over the detected communities
for community in communities:
    # Convert the set of nodes into a list and append it to the list of lists
    separated_communities.append(list(community))

# Initialise an empty list to store separated communities separated_communities = [] # Iterate over the detected communities for community in communities: # Convert the set of nodes into a list and append it to the list of lists separated_communities.append(list(community))

In [41]:

# Print or use the separated communities as needed
print(separated_communities)

# Print or use the separated communities as needed print(separated_communities)

[['NKX6-3', 'ZC2HC1B', 'ZSCAN10', 'HCG9', 'CC2D2B', 'DBX2', 'MOBP', 'STAP2', 'LCN2', 'ZNF462', 'TMEM72-AS1', 'LNCOC1', 'SLC28A2', 'SLC10A5', 'SRRM5', 'SLC17A7', 'OPA1-AS1', 'DEPDC7', 'LIN28A', 'SLC6A3', 'GJB6', 'TMEM255A', 'IGLC4', 'LINC00640', 'DENND6A-AS1', 'FNDC5', 'LAMA2', 'CYYR1', 'CNKSR3', 'RNF182', 'TECTA', 'KRT2', 'PRRT3-AS1', 'LINC02267', 'MUCL3', 'CFAP99', 'CCNA1', 'SLC26A8', 'GNG12', 'PHACTR3', 'LINC01133', 'C21orf62', 'ANKRD29', 'NGFR', 'NKD2', 'GJC2', 'LIM2', 'ANO1', 'LINC00997', 'STARD6', 'ARHGAP23', 'HYDIN', 'KLHL13', 'IGLV5-37', 'PLSCR2', 'TDRP', 'REG1A', 'LINC01832', 'ARHGEF39', 'CDH6', 'LINC01891', 'MGAM', 'AKAP14', 'TDRD1', 'PRLR', 'RARRES2', 'SLC2A4', 'OR2B11', 'DTNA', 'PTGES'], ['ACTN3', 'PDK4-AS1', 'C10orf105', 'ACVR2B-AS1', 'LINC02348', 'DPYD-IT1', 'UBE2Q2P16', 'PRKD3-DT', 'LINC01986', 'CALML6', 'EPHB2', 'PAPPA-AS1', 'DLGAP2', 'MROH8', 'RAB6C', 'ZNF503', 'H3C8', 'LINC02569', 'CDC42EP1', 'TFAP2A', 'ESCO2', 'WNT3A', 'SLC12A3', 'RGPD6', 'ICA1-AS1', 'FOXD3', 'LINC02615', 'FAM174A-DT'], ['IGHV3-32', 'LINC01050', 'STON2', 'CLGN', 'CCK', 'RGL3', 'COPDA1', 'PPP1R9A-AS1', 'SPDYE21', 'BSN', 'PRR15', 'IGKV3D-11', 'C12orf71', 'SMIM17', 'FAM20C', 'KCNQ4', 'PGAM2', 'DAGLA', 'NKX6-2', 'REEP1', 'LGALSL-DT', 'ZNF32-AS2', 'ZSCAN2-AS1', 'TWIST2', 'LINC01503', 'CADM4', 'DBH-AS1'], ['MAG', 'MOCS1', 'ALDH8A1', 'MTOR-AS1', 'MEX3B', 'MYO3B', 'GLP2R', 'SCT', 'TAF1L', 'IGHV3-73', 'OR2AK2', 'PTPRD-AS1', 'ST8SIA5', 'PITPNM2-AS1', 'EPHA2', 'TKTL2', 'SLC5A5', 'PCSK1', 'CUX2', 'IGHV3-69-1', 'ZNF474'], ['LINC02880', 'COL11A2', 'SCARF2', 'ADGRG3', 'ZNF491', 'CFAP141', 'FSTL1', 'TRBJ2-4', 'SMIM10L2B-AS1', 'UBL4B', 'CLEC1B', 'DPYSL4', 'LDHAL6A', 'PRUNE2', 'LINC00200', 'BRME1', 'FAM186B', 'VWA5B1', 'RARRES1', 'LINC01108'], ['SLC1A2-AS1', 'MIR130AHG', 'HEATR4', 'SLC49A3', 'OR6C6', 'SLC4A9', 'IGKV1D-13', 'ACTL7B', 'LINC01823', 'MIPOL1', 'AMPD1', 'IGKV2D-30', 'SLC16A14', 'DEPTOR-AS1', 'EDNRB-AS1', 'H3C12', 'LINC01990', 'ATP8A1-DT', 'TGFB2-AS1'], ['NLRP6', 'PRSS45P', 'NAALADL2', 'VSTM1', 'MYLK3', 'FOXI1', 'PCDHGA3', 'VWA7', 'HDHD5-AS1', 'LINC03021_ENSG00000254319', 'LINC01579', 'IGHV1-14', 'HCG22', 'LINC02055', 'UNC79', 'RNF217-AS1', 'C1orf50-AS1', 'GYS2'], ['CASC9', 'CCDC28A-AS1', 'TRPM1', 'CYP2S1', 'TMPRSS3', 'THTPA', 'GCNT3', 'FREY1', 'RHOXF1-AS1', 'NHS', 'IGHV7-4-1', 'SLITRK5', 'IGLV5-45', 'TRMT9B', 'CFAP57', 'RNF112', 'LINC00654'], ['ASIC3', 'SLC22A1', 'BHLHE22', 'LIF', 'S100A16', 'CT69', 'TRAV29DV5', 'C10orf71', 'TTLL7', 'MS4A4E', 'DNMBP-AS1', 'EDAR'], ['FAM182A', 'PACRG', 'NKX6-1', 'ACTA2-AS1', 'TAS2R39', 'CHRNG', 'LINC02660', 'CDH23'], ['TEKTIP1', 'ASGR2', 'IGKV2-26', 'LINC02057', 'GOLGA8H', 'LRRC49'], ['CYP2C8', 'PELP1-DT', 'LINC01301', 'CBY3', 'PTGR1'], ['KCNH6', 'LINC01980', 'DLG1-AS1', 'IQSEC2', 'LPAR4'], ['MYO3A', 'HSD17B2-AS1', 'DUOX2', 'LINC01115_ENSG00000237667'], ['FCN3', 'PCDHB4', 'S100A5'], ['USP43', 'IGFBP2', 'CNTNAP3'], ['NPM2', 'RHBDF1'], ['STXBP6', 'SERTAD3-AS1']]

In [42]:

len(communities2)

len(communities2)

Out[42]:

74

In [43]:

# Choose the index of the community you want to visualize
community_index2 = 0  # Change this to the index of the community you want to visualise

# Get the nodes in the selected community
selected_community2 = list(communities2[community_index2])

# Create a subgraph containing only the nodes and edges within the selected community
subgraph2 = G2.subgraph(selected_community2)

# Choose the index of the community you want to visualize community_index2 = 0 # Change this to the index of the community you want to visualise # Get the nodes in the selected community selected_community2 = list(communities2[community_index2]) # Create a subgraph containing only the nodes and edges within the selected community subgraph2 = G2.subgraph(selected_community2)

In [44]:

# Assuming subgraph is already defined
num_nodes = subgraph.number_of_nodes()
print(f"The number of nodes in the subgraph is: {num_nodes}")

# Assuming subgraph is already defined num_nodes = subgraph.number_of_nodes() print(f"The number of nodes in the subgraph is: {num_nodes}")

The number of nodes in the subgraph is: 70

In [45]:

#Step 7:
# Visualise the subgraph
pos = nx.spring_layout(subgraph2, k=0.8, iterations=20)  # You can use different layout algorithms if needed
plt.figure(figsize=(14, 12))
nx.draw(subgraph2, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8)
plt.title('Community Visualisation')
plt.show()

#Step 7: # Visualise the subgraph pos = nx.spring_layout(subgraph2, k=0.8, iterations=20) # You can use different layout algorithms if needed plt.figure(figsize=(14, 12)) nx.draw(subgraph2, pos, with_labels=True, node_color='skyblue', node_size=100, edge_color='gray', linewidths=0.1, font_size=8) plt.title('Community Visualisation') plt.show()